γ 3,∞
Jump to navigation
Jump to search
| γ ∞ 3 | |
|---|---|
| Rank | 3 |
| Dimension | 3 |
| Type | Regular |
| Space | Complex |
| Notation | |
| Coxeter diagram |     |
| Schläfli symbol | ∞{4}2{3}2 |
| Elements | |
| Faces | ∞ γ ∞ 2 |
| Edges | ∞ ∞-edges |
| Vertices | ∞ |
| Vertex figure | Triangle |
| Related polytopes | |
| Real analog | Cubic honeycomb |
| Dual | β ∞ 3 |
| Abstract & topological properties | |
| Flag count | ∞ |
| Properties | |
| Flag orbits | 1 |
γ ∞
3 is a regular complex polyhedron. It is a generalized cube.
Since its first generating mirror has infinite order, it does not meet some definitions of a complex polytope.[1]
Coxeter diagrams[edit | edit source]
A generalized square γ ∞
3 can be represented by the following Coxeter diagrams:
- (full symmetry)
(prism product of γ ∞
2 with an ∞-edge)- (prism product of three ∞-edges)
References[edit | edit source]
Bibliography[edit | edit source]
- Orlik, Peter; Reiner, Victor; Shepler, Anne (2002). "The sign representation for Shephard groups" (PDF). Mathematische Annalen. 322 (3): 477–492. arXiv:math/0011105. doi:10.1007/s002080200001.